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<div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">#!/usr/bin/python</span>
<a name="l00002"></a>00002 <span class="comment"># -*- coding: utf-8 -*-</span>
<a name="l00003"></a>00003 
<a name="l00004"></a>00004 <span class="comment"># Copyright (c) 2011</span>
<a name="l00005"></a>00005 <span class="comment">#</span>
<a name="l00006"></a>00006 <span class="comment"># Permission is hereby granted, free of charge, to any person obtaining a</span>
<a name="l00007"></a>00007 <span class="comment"># copy of this software and associated documentation files (the &quot;Software&quot;),</span>
<a name="l00008"></a>00008 <span class="comment"># to deal in the Software without restriction, including without limitation</span>
<a name="l00009"></a>00009 <span class="comment"># the rights to use, copy, modify, merge, publish, distribute, sublicense,</span>
<a name="l00010"></a>00010 <span class="comment"># and/or sell copies of the Software, and to permit persons to whom the</span>
<a name="l00011"></a>00011 <span class="comment"># Software is furnished to do so, subject to the following conditions:</span>
<a name="l00012"></a>00012 <span class="comment">#</span>
<a name="l00013"></a>00013 <span class="comment"># The above copyright notice and this permission notice shall be included in</span>
<a name="l00014"></a>00014 <span class="comment"># all copies or substantial portions of the Software.</span>
<a name="l00015"></a>00015 <span class="comment">#</span>
<a name="l00016"></a>00016 <span class="comment"># THE SOFTWARE IS PROVIDED &quot;AS IS&quot;, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR</span>
<a name="l00017"></a>00017 <span class="comment"># IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,</span>
<a name="l00018"></a>00018 <span class="comment"># FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE</span>
<a name="l00019"></a>00019 <span class="comment"># AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER</span>
<a name="l00020"></a>00020 <span class="comment"># LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,</span>
<a name="l00021"></a>00021 <span class="comment"># OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE</span>
<a name="l00022"></a>00022 <span class="comment"># SOFTWARE.</span>
<a name="l00023"></a>00023 <span class="comment">#</span>
<a name="l00024"></a>00024 <span class="comment"># Author: Jesus Carrero &lt;j.o.carrero@gmail.com&gt;</span>
<a name="l00025"></a>00025 <span class="comment"># Mountain View, CA</span>
<a name="l00026"></a>00026 <span class="comment">#</span>
<a name="l00027"></a>00027 
<a name="l00028"></a>00028 <span class="keyword">from</span> utils.Quadrature <span class="keyword">import</span> LegendreGaussQuadrature
<a name="l00029"></a>00029 <span class="keyword">from</span> GBMSolverAdaptor <span class="keyword">import</span> GBMSolverAdaptor
<a name="l00030"></a>00030 
<a name="l00031"></a>00031 
<a name="l00032"></a><a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html">00032</a> <span class="keyword">class </span><a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html">NumericalOptionGBM</a>(GBMSolverAdaptor):
<a name="l00033"></a>00033     <span class="stringliteral">&quot;&quot;&quot; main class to price derivaties under geometric brownian motion. &quot;&quot;&quot;</span>
<a name="l00034"></a>00034 
<a name="l00035"></a>00035     __slots__ = [<span class="stringliteral">&#39;m_opt_type&#39;</span>, <span class="stringliteral">&#39;m_contract_type&#39;</span>, <span class="stringliteral">&#39;m_greeks&#39;</span>,
<a name="l00036"></a>00036                  <span class="stringliteral">&#39;m_shape_func&#39;</span>, <span class="stringliteral">&#39;m_price_mode&#39;</span>]
<a name="l00037"></a>00037 
<a name="l00038"></a><a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#ace77dc114f06a395d62f588d92f829df">00038</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#ace77dc114f06a395d62f588d92f829df">__init__</a>(self, opt_type, time2_mat, prices, strikes,
<a name="l00039"></a>00039             ntime_steps, nsegs, smin=<span class="keywordtype">None</span>, smax=<span class="keywordtype">None</span>):
<a name="l00040"></a>00040         <span class="stringliteral">&quot;&quot;&quot; instantiate object of class NumericalOptionGBM.&quot;&quot;&quot;</span>
<a name="l00041"></a>00041         <span class="keywordflow">if</span> opt_type <span class="keywordflow">not</span> <span class="keywordflow">in</span> [<span class="stringliteral">&#39;A&#39;</span>, <span class="stringliteral">&#39;E&#39;</span>]:
<a name="l00042"></a>00042             <span class="keywordflow">raise</span> Warning(<span class="stringliteral">&#39;available pricing types: [American, European]&#39;</span>)
<a name="l00043"></a>00043 
<a name="l00044"></a>00044         self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#aeecbf5dfb1c1d5fbe9cb056dec6525ed">m_price_mode</a> = <span class="stringliteral">&#39;price-range&#39;</span>
<a name="l00045"></a>00045         (self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#ad52122459cad97c2129c959e64e18500">m_greeks</a>, self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#a2aa56fbf39ea7318382a50472431c2c4">m_shape_func</a>) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00046"></a>00046         (self.m_opt_type, self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#a442de3edd7bf536b723e495e84b9d886">m_contract_type</a>) = (opt_type, <span class="stringliteral">&#39;vanilla&#39;</span>)
<a name="l00047"></a>00047 
<a name="l00048"></a>00048         GBMSolverAdaptor.__init__(self, time2_mat, prices, strikes,
<a name="l00049"></a>00049                 ntime_steps, nsegs, smin, smax)
<a name="l00050"></a>00050 
<a name="l00051"></a><a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#a7070cfbfdaf275b8aa209bf73a781ce8">00051</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#a7070cfbfdaf275b8aa209bf73a781ce8">set_price_mode</a>(self, price_mode):
<a name="l00052"></a>00052         <span class="stringliteral">&quot;&quot;&quot; set price mode.&quot;&quot;&quot;</span>
<a name="l00053"></a>00053         <span class="keywordflow">if</span> price_mode <span class="keywordflow">not</span> <span class="keywordflow">in</span> [<span class="stringliteral">&#39;greeks&#39;</span>, <span class="stringliteral">&#39;price-range&#39;</span>, <span class="stringliteral">&#39;price&#39;</span>]:
<a name="l00054"></a>00054             <span class="keywordflow">raise</span> Warning(<span class="stringliteral">&#39;pricing modes: [greeks, price, price-range]&#39;</span>)
<a name="l00055"></a>00055         self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#aeecbf5dfb1c1d5fbe9cb056dec6525ed">m_price_mode</a> = price_mode
<a name="l00056"></a>00056 
<a name="l00057"></a>00057 
<a name="l00058"></a><a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#a9dfd0c8491a2ee26308d9d75b86a087d">00058</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#a9dfd0c8491a2ee26308d9d75b86a087d">set_contract_type</a>(self, contract_type):
<a name="l00059"></a>00059         <span class="stringliteral">&quot;&quot;&quot; set contract type.&quot;&quot;&quot;</span>
<a name="l00060"></a>00060         <span class="keyword">assert</span> contract_type <span class="keywordflow">in</span> [<span class="stringliteral">&#39;vanilla&#39;</span>, <span class="stringliteral">&#39;digital&#39;</span>]
<a name="l00061"></a>00061         self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#a442de3edd7bf536b723e495e84b9d886">m_contract_type</a> = contract_type
<a name="l00062"></a>00062 
<a name="l00063"></a>00063     <span class="keyword">def </span>_price_contract(self):
<a name="l00064"></a>00064         <span class="stringliteral">&quot;&quot;&quot; price derivative. &quot;&quot;&quot;</span>
<a name="l00065"></a>00065         <span class="keyword">assert</span> self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#a2aa56fbf39ea7318382a50472431c2c4">m_shape_func</a> <span class="keywordflow">is</span> <span class="keywordflow">not</span> <span class="keywordtype">None</span>
<a name="l00066"></a>00066         quads = <a class="code" href="classutils_1_1Quadrature_1_1LegendreGaussQuadrature.html">LegendreGaussQuadrature</a>(5)
<a name="l00067"></a>00067         self.set_sfunc_and_quads(self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#a2aa56fbf39ea7318382a50472431c2c4">m_shape_func</a>, quads)
<a name="l00068"></a>00068 
<a name="l00069"></a>00069         self.set_up_problem()
<a name="l00070"></a>00070         <span class="keywordflow">if</span> <span class="stringliteral">&#39;A&#39;</span> == self.m_opt_type:
<a name="l00071"></a>00071             self.set_constraint(self.get_pival())
<a name="l00072"></a>00072 
<a name="l00073"></a>00073         solution = self.solve()
<a name="l00074"></a>00074         self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#ad52122459cad97c2129c959e64e18500">m_greeks</a> = self._post_process(solution)
<a name="l00075"></a>00075 
<a name="l00076"></a>00076         self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#ad52122459cad97c2129c959e64e18500">m_greeks</a>[:, 3] = (self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#ad52122459cad97c2129c959e64e18500">m_greeks</a>[:, 3] - self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#ad52122459cad97c2129c959e64e18500">m_greeks</a>[:,
<a name="l00077"></a>00077                                2]) / self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#ad52122459cad97c2129c959e64e18500">m_greeks</a>[:, 0] ** 2
<a name="l00078"></a>00078         self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#ad52122459cad97c2129c959e64e18500">m_greeks</a>[:, 2] = self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#ad52122459cad97c2129c959e64e18500">m_greeks</a>[:, 2] / self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#ad52122459cad97c2129c959e64e18500">m_greeks</a>[:, 0]
<a name="l00079"></a>00079 
<a name="l00080"></a>00080         <span class="keywordflow">if</span> <span class="stringliteral">&#39;greeks&#39;</span> == self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#aeecbf5dfb1c1d5fbe9cb056dec6525ed">m_price_mode</a>:
<a name="l00081"></a>00081             <span class="keywordflow">return</span> (self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#ad52122459cad97c2129c959e64e18500">m_greeks</a>[:, 0], self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#ad52122459cad97c2129c959e64e18500">m_greeks</a>[:, 1:])
<a name="l00082"></a>00082         <span class="keywordflow">elif</span> <span class="stringliteral">&#39;price-range&#39;</span> == self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#aeecbf5dfb1c1d5fbe9cb056dec6525ed">m_price_mode</a>:
<a name="l00083"></a>00083             <span class="keywordflow">return</span> (self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#ad52122459cad97c2129c959e64e18500">m_greeks</a>[:, 0], self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#ad52122459cad97c2129c959e64e18500">m_greeks</a>[:, 1])
<a name="l00084"></a>00084         <span class="keywordflow">else</span>:
<a name="l00085"></a>00085             stpv = self.get_stock_pres_val()
<a name="l00086"></a>00086             (grid, price) = (self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#ad52122459cad97c2129c959e64e18500">m_greeks</a>[:, 0], self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#ad52122459cad97c2129c959e64e18500">m_greeks</a>[:, 1])
<a name="l00087"></a>00087             <span class="keywordflow">return</span> (price[grid &lt; stpv][-1] + price[stpv &lt;= grid][0]) / 2.
<a name="l00088"></a>00088 
<a name="l00089"></a><a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#a124788cf213a32f39a3a287f7fede521">00089</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#a124788cf213a32f39a3a287f7fede521">get_greeks</a>(self):
<a name="l00090"></a>00090         <span class="stringliteral">&quot;&quot;&quot; get greeks.&quot;&quot;&quot;</span>
<a name="l00091"></a>00091         <span class="keyword">assert</span> self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#ad52122459cad97c2129c959e64e18500">m_greeks</a> <span class="keywordflow">is</span> <span class="keywordflow">not</span> <span class="keywordtype">None</span>
<a name="l00092"></a>00092         <span class="keywordflow">return</span> self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#ad52122459cad97c2129c959e64e18500">m_greeks</a>
<a name="l00093"></a>00093 
<a name="l00094"></a><a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#a50ac59ec8459bfbb3194dd258ef60e38">00094</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#a50ac59ec8459bfbb3194dd258ef60e38">set_shape_functions</a>(self, shape_func):
<a name="l00095"></a>00095         <span class="stringliteral">&quot;&quot;&quot; set shape functions. &quot;&quot;&quot;</span>
<a name="l00096"></a>00096         self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#a2aa56fbf39ea7318382a50472431c2c4">m_shape_func</a> = shape_func
<a name="l00097"></a>00097 
<a name="l00098"></a><a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#a351f8905d163e18e9f960a706f786e65">00098</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#a351f8905d163e18e9f960a706f786e65">price_call</a>(self):
<a name="l00099"></a>00099         <span class="stringliteral">&quot;&quot;&quot;  price call contract. &quot;&quot;&quot;</span>
<a name="l00100"></a>00100         self.set_lbc(self._zero)
<a name="l00101"></a>00101         <span class="keywordflow">if</span> <span class="stringliteral">&#39;vanilla&#39;</span> == self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#a442de3edd7bf536b723e495e84b9d886">m_contract_type</a>:
<a name="l00102"></a>00102             self.set_ivalf(self._call_va_present_val)
<a name="l00103"></a>00103             self.set_rbc(self._ca_vanilla_rbc)
<a name="l00104"></a>00104         <span class="keywordflow">elif</span> <span class="stringliteral">&#39;digital&#39;</span> == self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#a442de3edd7bf536b723e495e84b9d886">m_contract_type</a>:
<a name="l00105"></a>00105             self.set_ivalf(self._call_di_present_val)
<a name="l00106"></a>00106             self.set_rbc(self._digital_bc)
<a name="l00107"></a>00107         <span class="keywordflow">else</span>:
<a name="l00108"></a>00108             <span class="keyword">assert</span> <span class="keyword">False</span>
<a name="l00109"></a>00109         <span class="keywordflow">return</span> self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#ab43aa6c08539aeba790a6aeaf1616ff6">_price_contract</a>()
<a name="l00110"></a>00110 
<a name="l00111"></a><a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#a059ea634022daa272cff71d647fa8646">00111</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#a059ea634022daa272cff71d647fa8646">price_put</a>(self):
<a name="l00112"></a>00112         <span class="stringliteral">&quot;&quot;&quot; price put contract.&quot;&quot;&quot;</span>
<a name="l00113"></a>00113         self.set_rbc(self._zero)
<a name="l00114"></a>00114         <span class="keywordflow">if</span> <span class="stringliteral">&#39;vanilla&#39;</span> == self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#a442de3edd7bf536b723e495e84b9d886">m_contract_type</a>:
<a name="l00115"></a>00115             self.set_ivalf(self._put_va_present_val)
<a name="l00116"></a>00116             self.set_lbc(self._put_va_lbc)
<a name="l00117"></a>00117         <span class="keywordflow">elif</span> <span class="stringliteral">&#39;digital&#39;</span> == self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#a442de3edd7bf536b723e495e84b9d886">m_contract_type</a>:
<a name="l00118"></a>00118             self.set_ivalf(self._put_di_present_val)
<a name="l00119"></a>00119             self.set_rbc(self._digital_bc)
<a name="l00120"></a>00120         <span class="keywordflow">else</span>:
<a name="l00121"></a>00121             <span class="keyword">assert</span> <span class="keyword">False</span>
<a name="l00122"></a>00122 
<a name="l00123"></a>00123         <span class="keywordflow">return</span> self.<a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html#ab43aa6c08539aeba790a6aeaf1616ff6">_price_contract</a>()
<a name="l00124"></a>00124 
<a name="l00125"></a>00125 
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